Relations, mappings and function notationIB MYP Maths Extended: Subtopic test

1. 1
   A function is defined by $f(x)=3x-4$.

   (a)

   Find $f(5)$.

   [1 mark]

   • A$19$
   • B$3$
   • C$15$
   • D$11$

   (b)

   Solve $f(x)=8$.

   [1 mark]

   • A$x=\frac43$
   • B$x=4$
   • C$x=12$
   • D$x=20$

   (c)

   Find $f(2a)$, giving your answer in its simplest form.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two relations are given as mappings. Relation $R$ maps $1\to4$, $2\to5$, $3\to5$ and $3\to6$. Relation $S$ maps $1\to4$, $2\to5$, $3\to5$ and $4\to5$.

   (a)

   Which statement about $R$ is correct?

   [1 mark]

   • A$R$ is a function because every input has an output.
   • B$R$ is not a function because the output $5$ is used twice.
   • C$R$ is not a function because the input $3$ has two outputs.
   • D$R$ is a function because it has four pairs.

   (b)

   Which statement about $S$ is correct?

   [1 mark]

   • A$S$ is a function because every input has exactly one output.
   • B$S$ is not a function because the output $5$ is repeated.
   • C$S$ is a function only if all the outputs are different.
   • D$S$ is not a function because it is not given by a formula.

   (c)

   Change one pair in $R$ so that it becomes a function, and explain why your new relation is a function.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A taxi company in Doha charges according to the rule $C(d)=5+2d$, where $C(d)$ is the cost in Qatari riyals (QAR) of a journey of $d$ kilometres.

   (a)

   (i) Find $C(12)$.
   (ii) Solve $C(d)=33$ and state what your answer means.

   [3 marks]

   (b)

   (i) State what $C(0)=5$ means, and what the number $2$ in the rule represents.
   (ii) A second company charges $D(d)=8+1.5d$ QAR. Find the distance for which both companies charge the same.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A scientist in Chile studies a glacial lake. The temperature $T$ in $^\circ$C of the water at a depth of $d$ metres is modelled by the function $T(d)=18-0.6d$. The model was designed for depths of up to 20 m.

   (a)

   (i) Find $T(10)$.
   (ii) Solve $T(d)=6$ to find the depth at which the temperature is $6^\circ$C.
   (iii) Explain what the numbers $18$ and $-0.6$ mean in this situation.

   [6 marks]

   (b)

   A second scientist suggests the model $U(d)=16-0.4d$.
   (i) Find the depth at which both models predict the same temperature.
   (ii) A measurement at a depth of 15 m gives $8.7^\circ$C. Calculate which model is closer to this measurement.
   (iii) A student uses $T$ to predict the temperature at a depth of 40 m. Justify why this prediction is unreliable.

   [6 marks]

   Total for question 4: 12 marks

End of questions